Electric Current basic definition doubt. PLEASE HELP.

[deepankvora]

1)I do understand why current must be same at all points in series as charge is conserved.
BUT, If a current, say 'I' is created in a loop, then why, exactly, do we say that the current in a part or element of the wire is the same, that is, 'I'?? Why is current independent of the length of wire we consider.
2)Also, if we define current through a cross-section, then why do we say that a current exists in a wire(conductor) of a finite length.

I have searched and thought a lot about it, and have also found solutions like the definition of current is rate of flow of charge, that is amount of charge passing a cross section in unit time. How does this conclude the problem?

This is not getting into my head and I can't understand this. PLEASE HELP.

 

[Doc Al]

I have searched and thought a lot about it, and have also found solutions like the definition of current is rate of flow of charge, that is amount of charge passing a cross section in unit time. How does this conclude the problem?

If you assume that charge is conserved--and that it doesn't build up at some point--then the flow rate of charge must be the same at every point in series.

 

[deepankvora]

If you assume that charge is conserved--and that it doesn't build up at some point--then the flow rate of charge must be the same at every point in series.

I do understand why current must be same at all points in series as charge is conserved.
BUT, why is the current in the length 'dl' of the wire same as the current in the full wire, that is 'L' length.
It is sort of confusing.

 

[Doc Al]

This statement:

I do understand why current must be same at all points in series as charge is conserved.

Seems to contradict this statement:

BUT, why is the current in the length 'dl' of the wire same as the current in the full wire, that is 'L' length.

The current is the same at all point in the wire, regardless of its length.

 

[deepankvora]

This statement:
Seems to contradict this statement:
The current is the same at all point in the wire, regardless of its length.

Sorry if I stated wrongly. I have attached a file. Kindly see.
What I mean is, I read that we define current as rate of flow of charge through a CROSS-SECTION. So, If we take many cross-sections (or points) on the wire, by conservation of charge, the current at those points must be same. Is that the reason why we say current in the WIRE and not cross section?
But, still, if current is there in a loop why and how do we say that the current in a chosen element or part of a wire is the same as the current flowing in the loop??
Thank you for replying and helping.
I will highly appreciate your further help and detailed explanation on this.

 

[Doc Al]

What I mean is, I read that we define current as rate of flow of charge through a CROSS-SECTION. So, If we take many cross-sections (or points) on the wire, by conservation of charge, the current at those points must be same. Is that the reason why we say current in the WIRE and not cross section?

When we talk about the current in the wire we mean through any cross section of the wire.

But, still, if current is there in a loop why and how do we say that the current in a chosen element or part of a wire is the same as the current flowing in the loop??

The current in the loop means the current in the wire, which is the same in every element of the wire.

Note that your "dl" is parallel to the wire and covers the entire cross-section.

 

[deepankvora]

the current in the wire, which is the same in every element of the wire.

Why is that so? why is current in the wire same as current in an element of the wire.

 

[jtbell]

Why do you think they might be different?

I would say that the fact that they are the same is simply a matter of definition. We define the current in a wire (or segment of wire) to be the current through any cross section of the wire (or segment).

 

[deepankvora]

Why do you think they might be different?

probably because the length is unequal

 

[mikeph]

Current is defined in terms of the rate of charge flowing through a unit area. Since that unit area has no thickness, the current on a circuit is defined at any individual point along the wire (the cross section being taken as perpendicular to the wire).

In this sense it is not rigorous to assign a current to an entire circuit, as it is not clear where the actual cross section is being taken. But this is fine in reality, because it's the same across EVERY cross section. So when I say "the current of this circuit is 5A", I mean, "the current across ANY cross section of this circuit is 5A", and it should not be taken to mean that current through a circuit involves some sort of integration over the length.

 

[deepankvora]

probably because the length is unequal

so for proving this, do we have to consider a crosssection in the dl element and say that it is a crosssection of the whole wire so it will have same current as the wire.
and because the crosssection of dl element has that current, the dl element will have the same current ?

if not, then how can we say so?

 

[Doc Al]

so for proving this, do we have to consider a crosssection in the dl element and say that it is a crosssection of the whole wire so it will have same current as the wire.
and because the crosssection of dl element has that current, the dl element will have the same current ?

I guess I'm still not understanding your question.

The first sentence of your initial post said it all:

1)I do understand why current must be same at all points in series as charge is conserved.

That's it in a nutshell. If the current--the charge passing each cross-section per second--were not the same at all points in the loop, then we'd have charge building up somewhere.

 

[mikeph]

The cross section is defined using dl, a local part of the wire. You cannot define a cross section for the entire wire. If I ask for the number of cars passing a certain point on a road, you're now asking me "how many cars pass over the entire length of the road?". It doesn't make sense.

The current at every point on the circuit is the same, due to charge conservation, so we say "the circuit has X current".

 

[deepankvora]

The cross section is defined using dl, a local part of the wire. You cannot define a cross section for the entire wire. If I ask for the number of cars passing a certain point on a road, you're now asking me "how many cars pass over the entire length of the road?". It doesn't make sense.

The current at every point on the circuit is the same, due to charge conservation, so we say "the circuit has X current".

alright, but if I take a wire of length L. Now how do we say that the current in the length, say x which is part of the wire, is the same(x is not a cross section, it is a finite length)?

 

[cabraham]

Electrons basically do not like each other. That is something I've heard for years. If an accumulation of electrons, or charges in general, take place, current would be reduced or even cease. A large build up of charges results in an E field which repels additional charges of like polarity.

Observation has shown that charges do not build up and that current entering a node equals current leaving. This is KCL.

The answers given above covered it pretty well.

Claude

 

[mikeph]

alright, but if I take a wire of length L. Now how do we say that the current in the length, say x which is part of the wire, is the same(x is not a cross section, it is a finite length)?

Current is defined in terms of a cross section. How would you go about finding a cross section from a finite length? If you can't (which you can't, but imagine trying), then it's a badly posed question, like "how many metres are in a cloud?".In the road analogy, your question is:

"if I take a road of length L. Now how do we say that the number of cars passing a point in the road in the length, say x which is part of the road, is the same(x is not a cross section, it is a finite length)?"

You are basically asking me how many cars pass a point in the road, over a 20 mile stretch of the road. It's a meaningless question.

 

[deepankvora]

Current is defined in terms of a cross section. How would you go about finding a cross section from a finite length? If you can't (which you can't, but imagine trying), then it's a badly posed question, like "how many metres are in a cloud?".


In the road analogy, your question is:

"if I take a road of length L. Now how do we say that the number of cars passing a point in the road in the length, say x which is part of the road, is the same(x is not a cross section, it is a finite length)?"

You are basically asking me how many cars pass a point in the road, over a 20 mile stretch of the road. It's a meaningless question.

so for proving this, do we have to consider a crosssection in the x length and say that it is a crosssection of the whole wire so it will have same current as the whole wire of length L.
and because the crosssection of x segment has that current, the x segment will have the same current ?

if not, then how can we say so?

 

[Born2bwire]

You can not define a cross-section for an entire volume. A cross-section is a surface, the entire wire is a volume. You can only define a cross-section along a plane, or, assuming that we are constricted to choosing planes normal to the length of the wire at any point, you can only define the cross-section at a single arbitrary point along the wire.

 

[deepankvora]

You can not define a cross-section for an entire volume. A cross-section is a surface, the entire wire is a volume. You can only define a cross-section along a plane, or, assuming that we are constricted to choosing planes normal to the length of the wire at any point, you can only define the cross-section at a single arbitrary point along the wire.

yeah, that's ok. what i said is:
let there be a wire of length L. Now how can you say that current in a part(segment) of it, say x be same?
My attempt at a proof is:
Consider a cross-section(plane) perpendicular in the part x. now, since this is also a cross-section of L length wire, by definition, current through will be same as current in L length. Now since the cross-section is common in both lenghts, the current in length x will also bethe same as current through the cross-section, and therefore equal to the current through the length L wire.

Is this correct? Or is there a better way to understand this that I am not able to get?

 

[Born2bwire]

Technically, you would need to prove equivalence of the current between every possible cross-section along the wire. Or equivalently, prove that the total currents are the same between any two arbitrary cross-sections. Current is technically a function of position along a wire, however, as others have stated previously, we can use charge conservation to show that the current along a continuous wire is the same at any point along the wire. Thus, we talk of the current in a wire as a single invariant value, disguising the actual underlying issue of current being a function of position.

 

[Dale]

I don't know if this helps, but it might be useful to remember the units. Current is charge/time. It is not directly related to either cross sectional area or volume. What you (the OP) are probably thinking of is current density which is current/area i.e. charge/(time area).

If charge does not accumulate in a given segment of wire and over a given interval of time then it is clear that the amount of charge that enters one end of the segment must be equal to the charge that leaves the opposite end of the segment over that time (the current). This is true regardless of the length, volume, cross sectional area, or other geometric properties of the wire. It is simple mass balance.